Question: A circle has a sector with area $2\pi$ and central angle $\dfrac{1}{4}\pi$ radian. What is the area of the circle? ${16\pi}$ $\color{#9D38BD}{\dfrac{1}{4}\pi}$ ${2\pi}$
Answer: The ratio between the sector's central angle $\theta$ and $2 \pi$ radians is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{2 \pi} = \dfrac{A_s}{A_c}$ $\dfrac{1}{4}\pi \div 2 \pi = 2\pi \div A_c$ $\dfrac{1}{8} = 2\pi \div A_c$ $A_c \times \dfrac{1}{8} = 2\pi$ $A_c = 2\pi \times 8$ $A_c = 16\pi$